# Simulation technique for slurries interacting with moving parts and deformable solids with applications

## Abstract

A numerical method for particle-laden fluids interacting with a deformable solid domain and mobile rigid parts is proposed and implemented in a full engineering system. The fluid domain is modeled with a lattice Boltzmann representation, the particles and rigid parts are modeled with a discrete element representation, and the deformable solid domain is modeled using a Lagrangian mesh. The main issue of this work, since separately each of these methods is a mature tool, is to develop coupling and model-reduction approaches in order to efficiently simulate coupled problems of this nature, as in various geological and engineering applications. The lattice Boltzmann method incorporates a large eddy simulation technique using the Smagorinsky turbulence model. The discrete element method incorporates spherical and polyhedral particles for stiff contact interactions. A neo-Hookean hyperelastic model is used for the deformable solid. We provide a detailed description of how to couple the three solvers within a unified algorithm. The technique we propose for rubber modeling/coupling exploits a simplification that prevents having to solve a finite-element problem at each time step. We also developed a technique to reduce the domain size of the full system by replacing certain zones with quasi-analytic solutions, which act as effective boundary conditions for the lattice Boltzmann method. The major ingredients of the routine are separately validated. To demonstrate the coupled method in full, we simulate slurry flows in two kinds of piston valve geometries. The dynamics of the valve and slurry are studied and reported over a large range of input parameters.

## Keywords

Discrete elements method Lattice Boltzmann Fluid–particle interaction Smagorinsky turbulence model Hyperelastic model Neo-Hookean elastic rubber model## Notes

### Acknowledgements

This work was supported by ARO Grant W911 NF-15-1-0598 and Schlumberger Technology Corporation. PM and KK would like to thank J.-Y. Delenne (INRA, UMR IATE Montpellier) for his helpful and useful discussions on DEM–LBM coupling and Sachith Dunatunga for his help in streamlining the numerics.

## Compliance with ethical standards

## Conflict of interest

The authors declare that they have no conflict of interest.

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